广义多值直觉模糊软集及其在多属性决策中的应用

软集理论作为一种处理不确定问题的数学新工具弥补了传统模糊理论在参数工具上的不足。本文将广义模糊软集与多值直觉模糊集相结合,提出了广义多值直觉模糊软集的概念,给出了广义多值直觉模糊软集的交、并、补、“且”、“或”运算的概念,并基于这些概念研究其若干相关性质。此外,还将广义多值直觉模糊软集应用到多属性决策问题中去,给出相应的算法。并进行实例分析说明该决策方法的可行性和有效性。     

带簇及矩形带簇的推广

本将带簇和矩形带簇的概念推广到了n-带簇εn=[x^n 1=x^n]和n-矩形带簇εn=[x^nyx^n=x^n]，讨论了这两种半群簇之间的关系，特别对所有n-带簇的并集ε=∪εn和所有n-矩形带簇的并集Rε=∪Rεn进行了研究．     

因素空间和范畴

本文讨论了几种模糊范畴的Ｔｏｐｏｓ性质，把集丛理论、范畴理论应用到因素空间的研究之中，建立了同一因素集上和不同因素集上的因素空间之间的关系，并给出了子因素空间的概念和子因素空间的布尔运算。     

模糊概念格

概念格是研究和处理概念内涵与外延确定性关系的数学方法 ,已成为一种有效的数据分析方法。本文进一步探讨概念内涵与外延的不确定关系的模糊映射 ,给出相应的隶属函数的一些基本数学性质 ,证明全体模糊概念构成一个完全格。     

拟阵与概念格的关系

本文以构造的方式建立起拟阵与概念格的联系,得到在同构意义下每个拟阵是一个概念格,但反之不然的结论;该结论使得利用概念格的性质研究拟阵成为现实,特别为将建造概念格的算法尤其是已计算机化的算法应用于求取拟阵奠定了基础,也为拟阵论成为研究概念格性质的辅助工具打下基础．     

基于因素空间理论的直觉模糊概念外延构建及其在决策中的应用

在因素空间理论基础上，提出直觉模糊概念，从原概念及其对立概念的表现外延出发，构造了直觉模糊概念外延的两种逼近，并在此基础上提出了基于反馈外延双层包络的DFE决策方法，最后，给出操作步骤并通过实例对上述理论方法进行了应用。     

基于粗糙集方法的概念格理论研究综述

概念格与粗糙集理论是软计算领域的两种不同方法,它们都在数据挖掘、知识工程、信息检索、人工智能、系统分析与管理决策等领域有重要应用。在介绍概念格基本概念的基础上,对近年来借助粗糙集方法研究概念格的粗糙集近似扩充、概念格的约简理论与方法、变精度概念格及基于概念格的模糊推理、概念粒计算系统的数学模型及迭代算法等方面进行了综述,并提出了进一步研究的问题和方向。     

原苏联高等数学教学改革的近况

<正> 近年来,哈尔滨工业大学数学系同乌克兰基辅工业大学应用数学系、高等数学教研室等单位建立了友好合作关系,多次派学者互访,进行学术与教学交流,了解到一些原苏联高等数学的教学改革情况,我们感到这些情况对于我们当前的高等数学的教学改革是有一定参考价值,所以我们想在本文中结合原苏联高等数学     

论数学概念的过度延伸

论数学概念的过度延伸朱文芳（首都师范大学数学系１０００３７）在数学概念教学中，经常说要让学生概念明确．所谓概念明确，是指明确概念的内涵和外延．内涵是概念质的方面，它说明概念所反映的事物特征．外延是概念的量的方面，它说明概念所反映的事物范围．学生学习概...     

质量、价格对顾客满意度的影响

关于质量、价格对顾客满意度的影响,尽管许多学者已经取得了显著的成就,但是这些研究都是基于定性分析,本部分转变研究角度,利用数学方法,分析质量、价格对顾客满意度的影响,给出顾客满意度和质量、价格的函数关系式;提出顾客满意度关于质量的弹性概念和顾客满意度关于价格的弹性概念,这样就可以从量化的角度来研究不同水平的质量或者不同价格对顾客满意度的影响及其非线性关系.     

Professional Development Strategically Connecting Mathematics and Science: The Impact on Teachers' Confidence and Practice

The press to integrate mathematics and science comes from researchers, business leaders, and educators, yet research that examines ways to support teachers in relating these disciplines is scant. Using research on science and mathematics professional development, we designed a professional development project to help elementary teachers improve their teaching of mathematics and science by strategically connecting these disciplines. The purposes of this study are: (a) to identify changes in teachers' confidence and practice after participating in the professional development and (b) to identify different ways to connect mathematics and science during the professional development. We use a Likert‐scale survey to assess changes in teachers' confidence related to teaching mathematics and science. In addition, we report on a thematic analysis of teachers' written responses to open‐ended questions that probed teachers' perceived changes in practice. We analyze field notes from observations of project workshops to document different types of opportunities for connecting mathematics and science. We conclude with implications for future professional development that connects mathematics and science in meaningful ways, as well as suggestions for future research.     

What Does Integration of Science and Mathematics Really Mean?

In this era of curriculum reconstruction, considerable attention is being focused on curriculum integration. The integration of science and mathematics continues to be interpreted in different ways. In this article, five different meanings of integration of science and mathematics–discipline specific, content specific, process, methodological and thematic–are investigated along with instructional implications of these different approaches to integration.     

Mathematics and life: lessons from history

Developments in mathematics, technology, science, culture and society are closely interwoven with each other. Beyond that, these interrelations tend to be very complex due to the multiplicity of factors involved. In this contribution, three examples from the human story are analysed in order to sensitize for possible characteristics of the interrelation. For the historical cases of early Mesopotamia, the Inca state and Renaissance Italy, it is demonstrated how specific socio-cultural conditions affect the development of mathematics and technology as well as their use. These findings lead to questions about our use of mathematics and the ways in which mathematics, society, technology, culture and science may be linked, today.     

Effectively coaching middle school teachers: A case for teacher and student learning

In this paper we report findings from a two-year, large-scale research project that describes the work of middle school mathematics specialists (also referred to as mathematics coaches or instructional coaches) who served in 10 school districts. We use mixed methods to describe how mathematics specialists spent their time supporting teachers and how these supports contributed to meaningful changes that teachers made in their instructional practices. We also report results that correlate student achievement scores with whether or not teachers were highly engaged with the mathematics specialists. We coordinate these quantitative results with findings from several case studies to illustrate the qualitatively different ways that mathematics specialists supported teachers’ ongoing work with their students. We also account for why some teachers participated more fully than others. Importantly, because mathematics specialists’ work was situated in different school settings with different demands, resources and administrative supports, these constraints and affordances contributed in part to how they could effectively support teachers’ work with their students.     

Preservice Elementary Teachers' Use of Mathematics in a Project‐Based Science Approach

The use of a project‐based science (PBS) approach to teaching encourages students to integrate mathematics and science in meaningful ways as they create projects. As a beginning study of how students use mathematics in such an approach, an analysis of 23 projects developed by preservice elementary teachers enrolled in an elementary science course was conducted. Findings showed that students made a number of different types of mathematical errors and underutilized data representation and summary forms. Implications included the importance of developing methods for supporting the use of mathematical tools in utilizing a project‐based approach and considering ways that such tools mediate scientific thinking.     

Conceptualizing inquiry-based education in mathematics

The terms inquiry-based learning and inquiry-based education have appeared with increasing frequency in educational policy and curriculum documents related to mathematics and science education over the past decade, indicating a major educational trend. We go back to the origin of inquiry as a pedagogical concept in the work of Dewey (e.g. 1916, 1938) to analyse and discuss its migration to science and mathematics education. For conceptualizing inquiry-based mathematics education (IBME) it is important to analyse how this concept resonates with already well-established theoretical frameworks in mathematics education. Six such frameworks are analysed from the perspective of inquiry: the problem-solving tradition, the theory of didactical situations, the realistic mathematics education programme, the mathematical modelling perspective, the anthropological theory of didactics, and the dialogical and critical approach to mathematics education. In an appendix these frameworks are illustrated with paradigmatic examples of teaching activities with inquiry elements. The paper is rounded off with a list of ten concerns for the development and implementation of IBME.     

Changing Assessment Practices in Science and Mathematics

One recommendation of the national reform movements in mathematics and science is to change the way students are assessed. In this article five formats of alternative assessment forms are described, and suggestions are given on how these methods can be implemented within science and mathematics classrooms. Benefits of each type of assessment are discussed and potential pitfalls are elucidated. Samples of the five formats, journal writing, open-ended problems, portfolios, interviews and performance assessments, are included.     

Functions: a modelling tool in mathematics and science

It is difficult for the students to transfer concepts, ideas and procedures learned in mathematics to a new and unanticipated situation in science. An alternative to this traditional transfer method stresses the importance of modelling activities in an interdisciplinary context between mathematics and science. In the paper we introduce a modelling approach to the concept of function in upper secondary school is introduced. We discuss pedagogical and didactical issues concerning the interplay between mathematics and science. The discussion is crystallized into a didactical model for interdisciplinary instruction in mathematics and science. The model is considered as an iterative movement with two phases: (1) the horizontal linking of the subjects: Situations from science are embedded in contexts which are mathematized by the students, (2) the vertical structuring in the subjects: The conceptual anchoring of the students' constructs from the horizontal linking in the systematic and framework of mathematics and science respectively.     

Sociocultural Factors Influencing Students' Learning in Science and Mathematics: An Analysis of the Perspectives of African American Students

The voices of African American students reveal sociocultural factors that influence their achievement in science and mathematics classes. Using a sociocultural theoretical framework ( Mercer & Covey, 1980 ), this ethnographic study interpreted the perspectives of five African American students as they discussed their learning experiences in science and mathematics classrooms. This framework acknowledges the vulnerability of the educational system to societal influences that inevitably assert cultural values and norms. The students' discussions provided insight into their beliefs about the varied ways in which sociocultural factors impact their learning in science and mathematics classrooms.     

增加应用实例的比例有利于高等数学教学效果的进一步提高

阐述了在高等数学教学中增加应用实例的重要性.由于高等数学理论体系中,绝大多数的定义、定理或性质的获得几乎都与实际应用有关,因此本文针对一元函数微积分,探讨了在高等数学教学中根据不同知识点具体引入不同应用背景实例的方法.